This paper presents a novel variational approach for optical flow estimation that integrates several key assumptions: grey value constancy, gradient constancy, and a discontinuity-preserving spatio-temporal smoothness constraint. The method avoids linearisations in the data terms to allow for large displacements and uses a consistent numerical scheme based on two nested fixed point iterations. The approach is theoretically grounded in a coarse-to-fine warping strategy, which has previously been used experimentally. The method is shown to be robust to parameter variations and noise, and it achieves significantly smaller angular errors compared to previous techniques. The paper also demonstrates that the warping technique can be theoretically justified as a numerical approximation method. The method is evaluated on both synthetic and real-world data, showing excellent performance in terms of accuracy and robustness. The results indicate that the method outperforms existing techniques, especially in handling large displacements and noise. The paper also highlights the importance of combining different assumptions in the energy functional to achieve high accuracy and robustness in optical flow estimation. The method is efficient and can be applied to real-world image data with good results. The paper concludes that high accuracy and theoretical understanding are not contradictory but rather complementary aspects of optical flow estimation.This paper presents a novel variational approach for optical flow estimation that integrates several key assumptions: grey value constancy, gradient constancy, and a discontinuity-preserving spatio-temporal smoothness constraint. The method avoids linearisations in the data terms to allow for large displacements and uses a consistent numerical scheme based on two nested fixed point iterations. The approach is theoretically grounded in a coarse-to-fine warping strategy, which has previously been used experimentally. The method is shown to be robust to parameter variations and noise, and it achieves significantly smaller angular errors compared to previous techniques. The paper also demonstrates that the warping technique can be theoretically justified as a numerical approximation method. The method is evaluated on both synthetic and real-world data, showing excellent performance in terms of accuracy and robustness. The results indicate that the method outperforms existing techniques, especially in handling large displacements and noise. The paper also highlights the importance of combining different assumptions in the energy functional to achieve high accuracy and robustness in optical flow estimation. The method is efficient and can be applied to real-world image data with good results. The paper concludes that high accuracy and theoretical understanding are not contradictory but rather complementary aspects of optical flow estimation.